Abstract

Dark energy, which constitutes about 73% of the total energy density and causes the Universe expansion to accelerate, is one of the most important open problems in physics. The nature of dark energy can be inferred from its effects on the evolution of the Universe and the growth of structures as it influences the distribution of galaxies and gas at cosmological scales at low and intermediate redshifts. To extract unbiased information from the large scale galaxy power spectrum, accurate models, encoding the distortions due to non-linear evolution, bias and redshift space distortions, are needed.
In this thesis I present a model for the full shape of the power spectrum and test its validity against a suite of 50 large volume, moderate resolution N-body dark matter simulations. My results indicate that this simple model provides an accurate description of the full shape of the dark matter and halo power spectrum, both in real and redshift space, for k<0.15 h/Mpc. Even though its application is restricted to large scales, this prescription can provide tighter constraints on the dark energy equation of state parameter w_{DE} than those obtained by modelling the baryonic acoustic oscillations signal only, where the information of the broad-band shape of the power spectrum is discarded.
I then apply this model to a measurement of the power spectrum of the distribution of about 90000 luminous red galaxies (LRGs) across 7646 deg^2 in the Northern Galactic Cap from the seventh data release of the Sloan Sky Digital Survey. The errors and mode correlations are estimated from the 160 LasDamas mock catalogues, created in order to simulate the LRG galaxies and the survey geometry. Using the galaxy distribution, in combination with the latest measurement of the temperature and polarisation anisotropy in the cosmic microwave background, the luminosity-distance relation from the largest available type 1a supernovae dataset and a precise determination of the local Hubble parameter, I obtain cosmological constraints for five different parameter spaces. The analysis performed in this thesis shows that the Universe is geometrically flat and composed by about 4% of baryons, 23% of cold dark matter and 73% of dark energy. I measure w_{DE} to be -1.025+-0.065 without any evidence of time dependence, which is compatible with a cosmological constant.
In the next years new experiments will allow to measure the clustering of galaxies with a precision much higher than today, and models like the one used here will provide valuable tools in order to achieve the full potentials of the observations and obtain unbiased constraints on the cosmological parameters.